Navier–Stokes Hydrodynamic Limit of BGK Kinetic Equations for an Inert Mixture of Polyatomic Gases

Abstract

We perform an hydrodynamic limit of BGK equations for an inert mixture of polyatomic gases, with molecular structure modelled by a set of discrete internal energy levels. An asymptotic Chapman–Enskog procedure provides consistent hydrodynamic equations at Navier–Stokes level for species number densities, global momentum and total (kinetic plus internal) energy. We explicitly compute diffusion velocities (with Fick matrix and Soret coefficients), pressure tensor (with the dynamical pressure typical of polyatomic gases), and heat flux (with Dufour effect).